Sinkhorn Linearization and the Spectral Proxy: Unifying the Statistical and Algorithmic Theory of Feature-Parameterized Inverse Optimal Transport via a Single Spectral Sandwich
arXiv:2608.13201
2026
Architecture
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper gives a constructive sensitivity and conditioning theory for entropic OT layers whose costs are linear in features. Its main transferable asset is a spectral sandwich that turns plan probabilities, entropy strength, and feature covariance into explicit lower bounds on the parameter-to-plan Jacobian and local strong convexity. This can be used to remove cost-function gauge directions, whiten identifiable parameters, and build conditioning-aware training rules for neural modules containing Sinkhorn operators. The strongest practical targets are differentiable OT layers, neural transport kernels, and inverse-OT objectives rather than generic networks.
Ideas from this paper
✗ Failed on benchmark
2026
Parameterize an entropic OT cost only in directions that can change the transport plan, removing row-plus-column potential directions that are invisible because of OT gauge invariance. Whiten the remaining feature coordinates using their empirical covariance, producing an OT layer whose identifiable parameters have substantially more uniform sensitivity.
Useful7/10
Difficulty5/10
Novelty7/10
Unverified
2026
Use the OT spectral bound as a conditioning signal for optimizing parameters of a neural cost or inverse-OT objective. Adapt the parameter step size and add a covariance floor whenever the estimated Jacobian lower bound collapses, preventing optimization from entering regions where Sinkhorn outputs become insensitive to the learned cost.
Useful6/10
Difficulty5/10
Novelty6/10